Category:Definitions/Homotopy Equivalences
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This category contains definitions related to Homotopy Equivalences.
Related results can be found in Category:Homotopy Equivalences.
Let $X$ and $Y$ be topological spaces.
Let $f: X \to Y$ be a continuous mapping.
Let there exist a continuous mapping $g: Y \to X$ such that:
- the composite mapping $g \circ f$ is homotopic to the identity mapping $I_X$ on $X$
- the composite mapping $f \circ g$ is homotopic to the identity mapping $I_Y$ on $Y$.
Then $X$ and $Y$ are homotopy equivalent.
Pages in category "Definitions/Homotopy Equivalences"
The following 3 pages are in this category, out of 3 total.